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C₂×#11334 #358482

• p-group
• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

1886 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 34 points:

(1,2);(3,4,8,12,9,13,7,23)(5,14,18,25,17,29,16,10)(6,11,22,26,21,27,20,33)(15,30,32,24,19,28,31,34);(3,5,7,16,9,17,8,18)(4,10,12,14,13,25,23,29)(6,19,20,32,21,15,22,31)(11,24,26,28,27,34,33,30);(3,6)(4,11)(5,15,17,19)(7,20)(8,22)(9,21)(10,24,25,34)(12,26)(13,27)(14,28,29,30)(16,31,18,32)(23,33)

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 265678);